Question:medium

There are two containers of the same volume,first container half-filled with sugar syrup and the second container half-filled with milk.Half the content of the first container is transferred to the second container,and then the half of this mixture is transferred back to the first container.Next, half the content of the first container is transferred back to the second container.Then the ratio of sugar syrup and milk in the second container is

Updated On: Jan 15, 2026
  • \(5\ratio6\)
  • \(5\ratio4\)
  • \(6\ratio5\)
  • \(4\ratio5\)
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The Correct Option is A

Solution and Explanation

Let the volume of each container be V.

Initially, both containers are half-filled:

  • First container: \( \frac{V}{2} \) sugar syrup
  • Second container: \( \frac{V}{2} \) milk

Step 1: Transfer half the content from the first to the second container

  • Sugar syrup transferred: \( \frac{V}{4} \)
  • Now, second container has:
    • Sugar syrup: \( \frac{V}{4} \)
    • Milk: \( \frac{V}{2} \)
  • Total in second container: \( \frac{3V}{4} \)

Step 2: Transfer half of this mixture back to the first container

  • Mixture transferred: \( \frac{3V}{8} \)
  • Proportions in the mixture:
    • Sugar syrup part: \( \frac{V}{4} \)
    • Milk part: \( \frac{V}{2} \)
  • Sugar syrup transferred back: \( \frac{V}{4} \times \frac{1}{2} = \frac{V}{8} \)
  • Milk transferred back: \( \frac{V}{2} \times \frac{1}{2} = \frac{V}{4} \)

Step 3: Transfer half of the first container back to the second

  • Now in first container:
    • Sugar syrup = remaining = \( \frac{V}{2} - \frac{V}{4} + \frac{V}{8} = \frac{5V}{8} \)
    • Milk = \( \frac{V}{4} \)
  • Total in first container = \( \frac{5V}{8} + \frac{V}{4} = \frac{7V}{8} \)
  • Half transferred = \( \frac{7V}{16} \)
  • Sugar syrup transferred = \( \frac{5V}{8} \times \frac{1}{2} = \frac{5V}{16} \)
  • Milk transferred = \( \frac{V}{4} \times \frac{1}{2} = \frac{V}{8} \)

Final content in the second container:

  • Existing sugar syrup = \( \frac{V}{4} \)
  • New sugar syrup added = \( \frac{5V}{16} \)
  • Total sugar syrup = \( \frac{9V}{16} \)
  • Remaining milk in second container = \( \frac{V}{2} - \frac{V}{4} = \frac{V}{4} \)
  • New milk added = \( \frac{V}{8} \)
  • Total milk = \( \frac{5V}{16} \)

Final Ratio:

\[\text{Sugar Syrup : Milk} = \frac{9V}{16} : \frac{5V}{16} = \frac{9}{5}\]

Final Answer: Ratio = \( \mathbf{9:5} \)

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The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
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